**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Equation solving

Summary

In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality.
A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set.
An equation may be solved either numerically or symbolically. Solving an equation numerically means that only numbers are admitted as solutions. Solving an equation symbolically means that expressions can be used for representing the

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications (3)

Loading

Loading

Loading

Related courses (41)

Related units

CS-420: Advanced compiler construction

Students learn several implementation techniques for modern functional and object-oriented programming languages. They put some of them into practice by developing key parts of a compiler and run time system for a simple functional programming language.

ME-332: Mechanical vibrations

Dans ce cours on étudie la dynamique modale des structures mécaniques. Conceptes clés comme Mode Normale, Mass et Raideur effective, et Fréquences Propres sont appris pendant ce cours.

ME-474: Numerical flow simulation

This course provides practical experience in the numerical simulation of fluid flows. Numerical methods are presented in the framework of the finite volume method. A simple solver is developed with Matlab, and a commercial software is used for more complex problems.

No results

Related concepts (30)

Equation

In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages

Algebra

Algebra () is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics.
Elementary algebra deals with the manipulation

Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form
:P = 0
where P is a polynomial with coefficients in some field, often the field of the rational nu

Related people

No results

The objective of this PhD thesis is the translation of, and the mathematical commentary on, a 16th-century Latin book. Its author, Diego Palomino is not well known. With a background in theology, he was a prior. In order to obtain his PhD at the University of Alcala (Madrid), he submitted a work, De mutations æris, in which he included a collection of what seems to be readings notes, entitled Fragmentum de inventionibus scientiarum. His readings have been drawn from various famous mathematicians of his time and ancient ones. The originality of his work relies mostly on his inventiveness and his style —which can be sarcastic— making the reading of it quite interesting and lively. His work consists for the main part in explaining some unclear demonstrations, or bringing new methods of solution ; he also innovates in solving pairs of indeterminate equations by providing the complete set of integral solutions. Before him, only one mathematician (Abu ̄ K ̄amil, at the end of the 10th century) did so, the other mathematicians restricting themselves to giving only one solution or a pair. Palomino did not hesitate in criticizing a well-established theory in ancient mathematics, namely Archimedes —although his critics seem to rely on a faulty edition. His book is entitled to have a significant place in the history of mathematics, for it both maintains the rigor of Greek classical mathematics and announces innovation, as did the 17th century, culminating with the discovery of the infinitesimal calculus.

This paper theoretically proposes a multichannel nonlocal metasurface computer characterized by generalized sheet transition conditions (GSTCs) and surface susceptibility tensors. The study explores polarization- and angle-multiplexed metasurfaces enabling multiple and independent parallel analog spatial computations when illuminated by differently polarized incident beams from different directions. The proposed synthesis overcomes substantial restrictions imposed by the previous designs such as large architectures arising from the need for additional sub-blocks; slow responses; working for a certain incident angle or polarization; executing only a single mathematical operation; and, most importantly, supporting only the even-symmetric operations for normal incidences. The versatility of our design is demonstrated in a way that an ultracompact, integrable, and homogeneous metasurface-assisted platform can execute a variety of optical-signal-processing operations such as spatial differentiation and integration. It is demonstrated that a metasurface featuring nonreciprocal properties can be thought of as a new paradigm to break the even symmetry of reflection and perform both even- and odd-symmetric mathematical operations for input fields coming from a normal direction. Numerical simulations also illustrate different aspects of a multichannel edge detection scheme through projecting multiple images on the metasurface from different directions. Such appealing findings not only circumvent the major potential drawbacks of previous designs but may also offer an efficient, easy-to-fabricate, and flexible approach in wave-based signal processing, edge detection, image contrast enhancement, hidden object detection, and equation solving without a Fourier lens.

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

Despite their widespread use for performing advanced computational tasks, digital signal processors suffer from several restrictions, including low speed, high power consumption and complexity, caused by costly analogue-to-digital converters. For this reason, there has recently been a surge of interest in performing wave-based analogue computations that avoid analogue-to-digital conversion and allow massively parallel operation. In particular, novel schemes for wave-based analogue computing have been proposed based on artificially engineered photonic structures, that is, metamaterials. Such kinds of computing systems, referred to as computational metamaterials, can be as fast as the speed of light and as small as its wavelength, yet, impart complex mathematical operations on an incoming wave packet or even provide solutions to integro-differential equations. These much-sought features promise to enable a new generation of ultra-fast, compact and efficient processing and computing hardware based on light-wave propagation. In this Review, we discuss recent advances in the field of computational metamaterials, surveying the state-of-the-art metastructures proposed to perform analogue computation. We further describe some of the most exciting applications suggested for these computing systems, including image processing, edge detection, equation solving and machine learning. Finally, we provide an outlook for the possible directions and the key problems for future research.

2020Related lectures (56)